Rotational Motion

1. Rotational Motion • Angular Measure (radian) • Angular Speed and velocity • Centripetal Acceleration • Centripetal Force • Angular Acceleration

3. Angular measure y x=r cos(q) r y y=r sin(q) q x x

4. Angular measure 2p radians = 360° y 1.0 radian = 57.3° s Q= radians r r s q x x

5. How far to the moon? • Early Greek scientists estimated that the earth’s diameter is 3.5 times larger than the moon’s. • If a penny covers up the moon when held 200 cm from your eye, How far is the moon from Earth? (the diameter of a penny is 1.9 cm)

6. Small angles h≈ s & r ≈ x r s h q x h/r ≈ s/r ≈ h/x Sin q ≈ q ≈ tan q

7. Angular speed and velocity • Average angular speed

9. Linear speed and angular speed r s h q x

11. Linear speed and angular speed r s h q x h/r ≈ s/r ≈ h/x Sin q ≈ q ≈ tan q

12. Angular acceleration

13. Angular acceleration

14. Circular Motion(with constant a)

15. Circular Motion(constant a)

17. Kinetic Energy

24. d

29. Torque

32. a=? T=?

33. St = Ia TR = 1/2MR2 (a/R) T= 1/2M a a=? T=? mg-T=ma mg- 1/2M a=ma mg= 1/2M a+ma mg= (1/2M +m)a mg (1/2M +m) T= 1/2M a SF=ma mg-T=ma a =

34. Work and Power